Geodesic
On a approach to the construction of characteristic function for cooperative differential games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 4, pp. 19-39

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The paper presents a novel approach to the construction of characteristic functions for cooperative differential games. The characteristic function of coalition $S$ is computed in two stages: first, optimal control strategies maximizing the total payoff of the players; next, the cooperative optimal strategies are used by the players from the coalition $S$ while the left-out players from $N \setminus S$ use the strategies minimizing the total payoff of the players from $S$. The characteristic function defined in this way is superadditive. In addition, it possesses a number of other useful properties. To illustrate this result we compute characteristic function for a specific differential game of pollution control.
Keywords: cooperative games, characteristic function, differential games, superadditivity. 
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     author = {Ekaterina V. Gromova and Leon A. Petrosyan},
     title = {On a approach to the construction of characteristic function for cooperative differential games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/MGTA_2015_7_4_a2/}
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Ekaterina V. Gromova; Leon A. Petrosyan. On a approach to the construction of characteristic function for cooperative differential games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 4, pp. 19-39. http://geodesic.mathdoc.fr/item/MGTA_2015_7_4_a2/